. The London, Edinburgh and Dublin philosophical magazine and journal of science . . of thetesting battery. lfg=0, Ki_CK2~B* If a key be also put in the galvanometer-circuit, and thebattery-key be first depressed and then, after a certain intervalof time, the galvanometer-key,we have Gotts method of com-paring capacities. This allowsthe condenser longer time tocharge; and if the galvano- -meter when its key is depressedshows no throw, it indicatesthat the potentials t\ and v2are equal, and that therefore K1=C as before. 2 If, however, either of the condensers has an appreciableleakage, the
. The London, Edinburgh and Dublin philosophical magazine and journal of science . . of thetesting battery. lfg=0, Ki_CK2~B* If a key be also put in the galvanometer-circuit, and thebattery-key be first depressed and then, after a certain intervalof time, the galvanometer-key,we have Gotts method of com-paring capacities. This allowsthe condenser longer time tocharge; and if the galvano- -meter when its key is depressedshows no throw, it indicatesthat the potentials t\ and v2are equal, and that therefore K1=C as before. 2 If, however, either of the condensers has an appreciableleakage, the result will be false by this method. Suppose the condenser K2 has an insulation-resistance R,that of Kj being infinite. On depressing the battery-key, asthe condensers are in series, they take initial charges eachequal to Q. Q=(V1-«1)K1 = (r1-V2)K2=(V1-V2)j&.2. Let an interval of time t elapse before the galvanometer-keyis depressed, and at the end of it let Qll and Q2 be the chargeson Kj and K2 respectively, and v the value of vx. Then t_ Q2 = Qe *,*, where <? = 2718,. and Q^,)-^ KiK2 --E5 K, Q1 = (V,-t.)K1={(Vx-V,)-(i;-V,)K1= {(V:-V2)-|}KJ( Now and Hence Also Comparing Capacities. 241 („-v2)=g=(v1-v2)E^E2^(v1-B)=g=(v1-v2)(i-1^-/-^). t v-V2= Kte ^R ^2-V2 C If, therefore, v = v2, or there appears to be a balance, tC _ K,e ^R B~ Ki(l-e K^R)+K or Ki = ^x • (B + C)e K^-G So that, unless t be made very small compared to K2R, wecannot compare K, and K2 unless we know R and t. In thecase of no leakage the conditions will be the same as if therewere no key in the galvanometer circuit. To find the best conditions for the test:—Taking equa-tion (2), and substituting for xx its value E D (A-f-DKB + C) C + DP+A+D+B+C TTT) which equals —7^—^r—^-tt;—~-, since AC = BD, we obtain EBD^) ^~{/^(C + D) + D(B^-C)}{G(B + C)+B(C^-D)}, If y=0, KsC^KiB. Suppose a fractional error p to be made in the value of CPhil. Mag. $. 5. Vol. 24. No. 148. Sept. 1887. R 242 Mr. E. C. Ei
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